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A token-based central queue with order-independent service rates

Abstract : We study a token-based central queue with multiple customer types. Customers of each type arrive according to a Poisson process and have an associated set of compatible tokens. Customers may only receive service when they have claimed a compatible token. If upon arrival, more than one compatible token is available, an assignment rule determines which token will be claimed. The service rate obtained by a customer is state-dependent, i.e., it depends on the set of claimed tokens and on the number of customers in the system. Our first main result shows that, provided the assignment rule and the service rates satisfy certain conditions, the steady-state distribution has a product form. We show that our model subsumes known families of models that have product-form steady-state distributions including the order-independent queue of [20] and the model of [22]. Our second main contribution involves the derivation of expressions for relevant performance measures such as the sojourn time and the number of customers present in the system. We apply our framework to relevant models, including an M/M/K queue with heterogeneous service rates, the MSCCC queue and multi-server models with redundancy. For some of these models, we present expressions for performance measures that have not been derived before.
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https://hal.archives-ouvertes.fr/hal-02934633
Contributor : Ina Maria Verloop Connect in order to contact the contributor
Submitted on : Wednesday, September 9, 2020 - 3:05:47 PM
Last modification on : Monday, July 4, 2022 - 4:43:41 PM
Long-term archiving on: : Thursday, December 3, 2020 - 1:09:13 AM

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Urtzi Ayesta, Tejas Bodas, Jan-Pieter Dorsman, Ina Maria Maaike Verloop. A token-based central queue with order-independent service rates. Operations Research, INFORMS, 2022, 70 (1), ⟨10.1287/opre.2020.2088⟩. ⟨hal-02934633⟩

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